$11$

$($SECTION $1\mathrm{.}3)$

$1\mathrm{.}3\mathrm{.}1.$ Derive the relationship between specific weight and density starting with Newton's $2^{nd}$ Law ma or alternatively, $W=mg.$

$1\mathrm{.}3\mathrm{.}2.$ Mexican crude oil has a specific gravity of $0\mathrm{.}976$ at $15\mathrm{.}5C.$ Determine its specific weight $($in $\frac{N}{m^3})$ and density $($in $k\frac{g}{m^3})$ at that temperature.

$1\mathrm{.}3\mathrm{.}3.$ The specific weight of a liquid is $55\mathrm{.}5l\frac{b}{f}{t}^3.$ Determine the weight, density, and specific gravity of the liquid if it occupies a volume of $20f{t}^3.$ Provide results in both the British system and S$.$I. units.

$1\mathrm{.}3\mathrm{.}4.$ A container has a $5m^3$ volume capacity and weighs $1500$ N when empty and $47,000N$ when filled with a liquid. What is the mass density and specific gravity of the liquid?

$1\mathrm{.}3\mathrm{.}5.$ A $2\mathrm{.}5-$ft$-$diameter cylindrical water tank $($Figure P$1\mathrm{.}3\mathrm{.}5)$ is suspended vertically by its sides. The tank contains water $(20C)$ to a depth $d.$ The force on the bottom of the tank is $920$ pounds. Determine the depthrof the water in the tank.

$1\mathrm{.}3\mathrm{.}6.$ A rocket carrying a specific volume of water weighing $8\mathrm{.}83$ kN on Earth lands on the Moon where the gravitational acceleration is one$-$sixth of that of the Earth. Find the mass and the Moon$-$weight of the water.

$1\mathrm{.}3\mathrm{.}7.$ Determine the change in volume of $100m^3$ of water contained in a swimming pool as it warms from $10C$ in the spring to $30C$ in the summer.

$1\mathrm{.}3\mathrm{.}8.$ The unit of energy in the SI system is a Newton$-$meter $($or Joule$).$ Determine the conversion factor for one unit of energy in this system to the B$.$G$.$ system $($foot$-$pound$).$ Check your result by looking in the front jacket of the book.

$1,3\mathrm{.}9.$ The unit of pressure in the SI system is a Pascal $(\frac{N}{m^2}).$ Determine the conversion factor for one unit of pressure in this system to the British system $($pounds per square inch, psi$).$ Check your result by looking in the front jacket of the book.

Help with questions $3\mathrm{.}2/3\mathrm{.}4/3\mathrm{.}5/3\mathrm{.}7$ please